2025/12/02 by Yunlong Xiao, Xiao, Yunlong
Computer Science · Physics and Astronomy · #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum many-body systems
paper · pdf · doi:10.48550/arxiv.2512.02493
Quantum channels function as the operational primitives of quantum theory, while superchannels describe the most general transformations acting upon them. Yet the prevailing framework for superchannels is both internally inconsistent, owing to the coexistence of distinct Choi operator constructions, and structurally incomplete, lacking the analogue of representations that ground channel theory. We resolve these issues by combining tensor-network methods with a generalized Occam's razor introduced here, establishing a unified foundation for superchannels. Our framework establishes the connections between competing Choi formulations, develops the Kraus, Stinespring, and Liouville representations for superchannels, and provides a simplified derivation of the realization theorem that identifies the minimal memory required to implement a given transformation. These structural tools also enable characterizations of superchannels that destroy quantum correlations or causal structure, opening a systematic route to non-Markovian quantum dynamics.